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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1998: STACS 98 pp 73–83Cite as

Searching constant width mazes captures the AC 0 hierarchy

  • Complexity I
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

Abstract

We show that searching a width k maze is complete for Π k, i.e., for the k'th level of the AC 0 hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for Π k. As an application, we show that there is a data structure solving dynamic st-connectivity for con stant width grid graphs with time bound O(log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.

Supported by the ESPRIT Long Term Research Programme of the EU under project number 20244 (ALCOM-IT).

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Massachusetts, USA

    David A. Mix Barrington & Chi-Jen Lu

  2. BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, USA

    Peter Bro Miltersen & Sven Skyum

Authors
  1. David A. Mix Barrington
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  2. Chi-Jen Lu
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  3. Peter Bro Miltersen
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  4. Sven Skyum
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Barrington, D.A.M., Lu, CJ., Miltersen, P.B., Skyum, S. (1998). Searching constant width mazes captures the AC 0 hierarchy. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028550

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  • DOI: https://doi.org/10.1007/BFb0028550

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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